Method and system for a boosted engine

ABSTRACT

Methods and systems are provided for coordinated control of a compound boosting system, including a first compressor staged upstream of a second compressor in an engine intake. In one example, a method may include operating the second, downstream compressor in steady-state to achieve an overall pressure ratio across the compound boosting system while operating the first, upstream compressor transiently, based on an airflow shortfall at the downstream compressor. A timing and amount of electric assistance provided to transiently operate the first, upstream compressor may be adjusted dynamically as the pressure ratio across the second compressor changes.

FIELD

The present description relates generally to methods and systems for aboosted engine system having staged charge boosting devices.

BACKGROUND/SUMMARY

Engines may be configured with boosting devices, such as turbochargersor superchargers, to increase airflow into a combustion chamber.Turbochargers and superchargers compress intake air entering the engineusing an intake compressor. While a turbocharger includes a compressorthat is mechanically driven by an exhaust turbine, an electricsupercharger includes a compressor that is electrically driven by amotor. In some engine systems, one or more intake charging devices maybe staged in series or parallel in what may be referred to as a compoundboosting configuration. For example, a fast, auxiliary boosting device(e.g., the electric supercharger) may be utilized to increase thetransient performance of a slower, primary boosting device (e.g., theturbocharger). In such a configuration, the turbocharger may be upsizedto increase peak power and torque performance of the engine, whichenables more aggressively downsized engines.

Various approaches may be used to provide boost control in a compoundboosting system. One example approach for compound boosting systemcontrol using pressure ratios is shown by Petrovic et al. in EP1,927,739 A1. The pressure ratio may represent the boosting capabilityof a boosting device of the compound boosting system. In the approach ofPetrovic, a method for coordinating two turbochargers based on desiredpartial pressure ratios is disclosed. Specifically, the desired partialpressure ratios for each turbocharger are determined based on calibratedlook-up tables using engine speed and engine torque as inputs. Thedesired partial pressure ratios are then achieved through at least oneof adjusting a turbocharger wastegate opening, adjusting turbine vanegeometry (e.g., if a variable geometry turbine is included), andadjusting openings of turbine and/or compressor bypasses.

However, the inventors herein have recognized potential issues with suchsystems. As one example, it is a static approach that uses predefinedcalibrations to determine the desired partial pressure ratios, which maybe independent of one another (e.g., the desired partial pressure ratioof one compression device does not influence the desired partialpressure ratio of the other compression device). If the approach ofPetrovic were applied to a compound boosting system including anelectric supercharger staged alongside a turbocharger, the approach maycause the supercharger to be run for a longer than required duration,resulting in a drop in fuel economy. As another example, the pressureratios commanded to each compression device may be calibratedconservatively in order to minimize boost pressure overshoot. However,this can result in a slower boost response. Further still, if any of thecompression devices are configured with electric assist (such aselectric assist from an electric motor/generator coupled to asupercharger compressor, a turbocharger compressor, or a turbochargershaft), opening of an exhaust waste-gate responsive to the boostpressure overshoot may represent a lost opportunity for energyrecuperation at the electric motor/generator.

In one example, the issues described above may be addressed by a methodcomprising: adjusting operation of a first intake compression devicebased on a target boost pressure; commanding positive torque from anelectric motor to a second intake compression device when a differencebetween a throttle inlet pressure and the target boost pressure ishigher than a threshold; and commanding negative torque from theelectric motor to the second intake compression device when thedifference is smaller than the threshold. In this way, a target boostpressure can be reached faster while increasing the energy recuperationopportunity of the electric motor.

As one example, a compound boosting system may include an upstream,faster-acting, auxiliary compressor configured with electric assistance(e.g., an electric supercharger compressor) and a downstream,slower-acting, primary compressor (e.g., a turbocharger compressor).Responsive to an operator torque demand, an engine controller maydynamically allocate pressure ratios to each compressor to provide atarget boost pressure. In particular, an overall pressure ratio commandmay be aggressively generated for the turbocharger. The overall pressureratio command may include corresponding adjustments to an opening of anexhaust waste-gate valve coupled in a waste-gate across the turbochargerturbine. For example, as the torque demand increases, the waste-gateopening may be decreased more aggressively to direct more exhaust flowthrough the turbine, spinning up the turbine to spin up the turbochargercompressor. However, due to the inherently slower response time of theturbocharger, there may be a temporary shortfall in boost availability,as indicated by a higher than threshold difference between the targetboost pressure and a throttle inlet pressure (or the outlet pressure ofthe turbocharger compressor). The shortfall may be addressed by spinningup the electric supercharger using positive torque from an electricmotor. When the shortfall decreases, such as when there is a lower thanthreshold difference between the target boost pressure and the throttleinlet pressure, but before the throttle inlet pressure reaches thetarget boost pressure, the electric assistance may be disabled and themotor may be used as a generator to absorb torque from the compressor.By adjusting a timing of when the electric assistance is disabled, thethrottle inlet pressure may be coasted towards the target boost pressurewithout incurring any overshoots, while at the same time, energy can berecuperated at the electric motor. It will be appreciated that while theexample is described with reference to an electric supercharger, it isnot meant to be limiting, and the same approach may be used for analternate compression device configured with electric assistance, suchas an electric turbocharger.

In this way, by more aggressively calibrating a pressure ratio commandedto each of a higher frequency auxiliary compressor configured withelectric assistance as well as a lower frequency primary compressor, atarget boost pressure may be achieved more efficiently. By commanding apositive speed output to an electric motor providing the electricassistance when the actual boost pressure is further from the targetboost pressure, a transient boost response may be improved. Thetechnical effect of commanding a negative speed output to the electricmotor when the actual boost pressure is closer to, but not yet at, thetarget boost pressure, is to reduce boost overshoot, while maximizingthe energy recuperation ability of the electric motor. Overall, boostpressure can be provided rapidly and more efficiently.

It should be understood that the summary above is provided to introducein simplified form a selection of concepts that are further described inthe detailed description. It is not meant to identify key or essentialfeatures of the claimed subject matter, the scope of which is defineduniquely by the claims that follow the detailed description.Furthermore, the claimed subject matter is not limited toimplementations that solve any disadvantages noted above or in any partof this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example embodiment of a compound boosted engine systemhaving multiple staged intake compression devices.

FIG. 2 depicts a high-level flow chart for dynamically allocatingpressure ratios between each of multiple intake compression devices in acompound boosted engine system, and adjusting motor torque delivery tothe intake compression device configured with electric assist using alead compensator.

FIG. 3 depicts an example dynamic pressure ratio allocation between anelectric supercharger and a turbocharger control during a vehicleacceleration event.

FIG. 4 depicts an example system response using a lead compensator.

FIG. 5 depicts an example block diagram of a boost control architectureincluding dynamic pressure ratio allocation and lead compensationabilities.

FIG. 6 depicts an example method for boost control by coordinatingoperation of a turbocharger and an electric supercharger using dynamicpressure ratio allocation and lead compensation.

FIG. 7 shows a map with example acceleration trajectories according tothe present disclosure.

FIG. 8 depicts a prophetic example of turbocharger and electricsupercharger pressure ratio coordination during vehicle operation.

DETAILED DESCRIPTION

The following description relates to systems and methods for boostcontrol in an engine system having staged boosting devices, wherein atleast one of the boosting devices is configured with electric assist.One non-limiting example of such a boosted engine system is shown inFIG. 1, wherein a turbocharger is staged downstream of an electricsupercharger. Boost control in the compound boosting system may beachieved by dynamically allocating distinct pressure ratio commands toeach compression device, and by further using lead compensation toreduce pressure overshoots. An engine controller may be configured toperform a control routine, such as the example routine of FIG. 2, viathe control architecture of FIG. 5, to allocate a pressure ratio to theslower-acting compression device based on the torque demand, whileallocating a pressure ratio to the faster-acting compression device(with electric assist) based on an air-flow shortfall. In addition, thecontroller may use a lead compensator to determine when to increase anddecrease electric assistance from an electric motor so as to reducepressure overshoots. One example approach that may be applied in theengine system of FIG. 1 is shown at the example routine of FIG. 6. As aresult of the dynamic pressure ratio allocation, a target boost pressuremay be achieved in a shorter amount of time and with reduced reliance onelectric assistance, as shown at FIG. 3. As a result of the leadcompensation, boost pressure overshooting may be reduced whilemaximizing energy recuperation opportunities at an electric motor, asshown at FIG. 4. By relying on these approaches, an accelerationtrajectory, such as shown in FIG. 7, can be improved. A propheticexample of coordinating turbocharger and electric supercharger operationbased on pressure ratios during vehicle operation is shown in FIG. 8.

FIG. 1 schematically shows aspects of an example engine system 100,including an engine 10 coupled in a vehicle 102. In some examples,vehicle 102 may be a hybrid vehicle with multiple sources of torqueavailable to one or more vehicle wheels 47. In other examples, vehicle102 is a conventional vehicle with only an engine. In the example shown,a powertrain of vehicle 102 includes engine 10 and an electric machine52. Electric machine 52 may be a motor or a motor/generator. Engine 10and electric machine 52 are connected to vehicle wheels 47 via atransmission 48 when one or more clutches 53 are engaged. In thedepicted example, a (first) clutch 53 is provided between engine 10 andelectric machine 52, and a (second) clutch 53 is provided betweenelectric machine 52 and transmission 48. A controller 12 may send asignal to an actuator of each clutch 53 to engage or disengage theclutch, thereby connecting or disconnecting engine 10 from electricmachine 52 and the components connected thereto and/or connecting ordisconnecting electric machine 52 from transmission 48 and thecomponents connected thereto. For example, torque from engine 10 may betransferred to vehicle wheels 47 via a crankshaft 40, transmission 48,and a powertrain shaft 84 when clutches 53 are engaged. Transmission 48may be a gearbox, a planetary gear system, or another type oftransmission. Transmission 48 may be a fixed ratio transmission thatincludes a plurality of gear ratios to allow engine 10 to rotate at adifferent speed than wheels 47. By changing a torque transfer capacityof first clutch 53 (e.g., an amount of clutch slippage), an amount ofengine torque relayed to the wheels via powertrain shaft 84 may bemodulated.

The powertrain may be configured in various manners, including as aparallel, a series, or a series-parallel hybrid vehicle. In electricvehicle embodiments, a system battery 45 may be a traction battery thatdelivers electrical power to electric machine 52 to provide torque tovehicle wheels 47. In some embodiments, electric machine 52 may also beoperated as a generator to provide electrical power to charge systembattery 45, for example, during a braking operation. It will beappreciated that in other embodiments, including non-electric vehicleembodiments, system battery 45 may be a typical starting, lighting,ignition (SLI) battery coupled to an alternator 46.

Alternator 46 may be configured to charge system battery 45 using enginetorque drawn from the crankshaft during engine running. In addition,alternator 46 may power one or more electrical systems of the engine,such as one or more auxiliary systems including a heating, ventilation,and air conditioning (HVAC) system, vehicle lights, an on-boardentertainment system, and other auxiliary systems, as described furtherbelow, based on their corresponding electrical demands. In one example,a current drawn on the alternator may continually vary based on each ofan operator cabin cooling demand, a battery charging requirement, otherauxiliary vehicle system demands, and motor torque. A voltage regulatormay be coupled to alternator 46 in order to regulate the power output ofthe alternator based upon system usage requirements, including auxiliarysystem demands.

In the depicted embodiment, engine 10 is a compound boosted engineconfigured with multiple, staged boosting devices. Specifically, engine10 includes a first boosting device staged upstream of a second boostingdevice. Herein, the first boosting device is an auxiliary boostingdevice and the second boosting device is a primary boosting device,although other configurations may be possible. The depictedconfiguration results in a first compressor 110 (of the first boostingdevice) being positioned in an engine intake passage 42 upstream of asecond compressor 114 (of the second boosting device). At least one ofthe boosting devices may be configured with electric assistance from anelectric motor. In the present example, the first boosting device is anelectric supercharger 13 configured to operate with electric assistancefrom an electric motor, while the second boosting device is aturbocharger 15. However, other combinations and configurations ofboosting devices may be possible without departing from the scope ofthis disclosure. For example, in alternate embodiments, turbocharger 15may be an electric turbocharger having an electric motor coupled to thecompressor, turbine, or turbocharger shaft while the supercharger isconfigured as an electrical or mechanical supercharger. In still otherexamples, both the first and second boosting device may be electricsuperchargers or electric turbochargers.

In the depicted example, electric supercharger 13 includes firstcompressor 110, which is driven by an electric motor 108. Specifically,a fan of first compressor 110 may be driven by power received fromelectric motor 108 along a supercharger compressor shaft 80. In someexamples, first compressor 110 of supercharger 13 may additionally bedriven by the engine crankshaft via a clutch and gear mechanism.Electric motor 108 may be powered by an on-board energy storage device,such as system battery 45. Electric motor 108 may be additionally oralternatively powered by alternator 46. An amount of electrical powerdelivered to electric motor 108 may be varied in order to adjust a dutycycle of the supercharger. In one example, the amount of electric powerdelivered to electric motor 108 may be increased to increase the speedof first compressor 110, with a corresponding increase in the electricalload applied on the alternator and a decrease in alternator current. Asa result of the electrical assistance, supercharger 13 may be rapidlyspun up, providing for a fast-acting or high frequency boost actuation.

During selected conditions, air may enter first compressor 110 when theopening of an electric supercharger bypass valve (ESBV) 72 is decreased,thereby directing incoming air from an air box 112 through a firstcompressor bypass passage 70 and first compressor 110, where it ispressurized for delivery to the second compressor 114. Fresh airreceived at an inlet of second compressor 114 is then compressed andintroduced into engine 10. As the opening of ESBV 72 increases, anamount of air entering second compressor 114 without having passedthrough first compressor bypass passage 70 and first compressor 110increases. During conditions when ESBV 72 is fully opened, compressedair may be delivered to engine 10 via second compressor 114 ofturbocharger 15 only. By spinning up the electric supercharger via theelectric motor, a burst of boost pressure may be rapidly provided to theengine.

Electric motor 108 may be configured as a motor-generator. Thus, duringconditions when electric assistance is required for boost build-up, theelectric motor may provide positive torque to drive either thecentrifugal compressor of the supercharger (or the turbocharger shaft)to improve the transient boost pressure delivery. However, the electricmotor is also capable of energy recuperation by “braking” the motorshaft. Therein, negative torque may be applied to the compressor (orshaft), reducing the compressor speed and concurrently charging thesystem battery (such as battery 45) coupled to the motor. As elaboratedwith reference to FIG. 2, an engine controller may control a timing andamount of positive torque and negative torque applied from the electricmotor to the supercharger so as to regulate a Throttle Inlet Pressure(TIP)/boost pressure.

Turbocharger 15 includes second compressor 114, which is driven by aturbine 116. Second compressor 114 is shown as a turbocharger compressormechanically coupled to turbine 116 via a shaft 19, the turbine 116driven by expanding engine exhaust. In one embodiment, the turbochargermay be a twin scroll device. In another embodiment, the turbocharger maybe a variable geometry turbocharger (VGT), wherein turbine geometry isactively varied as a function of engine operating conditions.

Fresh air is introduced along intake passage 42 into engine 10 via airbox 112 and flows to second compressor 114. During selected conditions,as elaborated below, air compressed by turbocharger 15 may berecirculated from an outlet to an inlet of second compressor 114 througha second compressor bypass passage 60 by adjusting an opening of acompressor recirculation valve (CRV) 62. CRV 62 may be a continuouslyvariable valve, and increasing the opening of the CRV 62 may includeactuating (or energizing) a solenoid of the valve.

One or both of CRV 62 and ESBV 72 may be continuously variable valveswherein a position of the valve is continuously variable from a fullyclosed position to a fully open position. Alternatively, CRV 62 may be acontinuously variable valve while ESBV 72 is an on-off valve. In someembodiments, CRV 62 may be partially open during boosted engineoperation to provide a surge margin. Herein, the partially open positionmay be a default valve position. Then, in response to an indication ofsurge, the opening of CRV 62 may be increased. For example, CRV 62 maybe adjusted from the default, partially open position toward a fullyopen position, with a degree of opening based on the indication of surge(e.g., the compressor ratio, the compressor flow rate, a pressuredifferential across the compressor, etc.). In alternate examples, CRV 62may be held closed during boosted engine operation (e.g., peakperformance conditions) to decrease boost response time and increasepeak performance.

Second compressor 114 is coupled to a throttle valve 20 through acharge-air cooler (CAC) 18 (also referred to as an intercooler herein).Air flows from second compressor 114 through CAC 18 and throttle valve20 to an intake manifold 22. CAC 18 may be an air-to-air or water-to-airheat exchanger, for example. Intake manifold pressure (e.g., a pressureof the air charge within the intake manifold) may be determined using amanifold absolute pressure (MAP) sensor 124.

Intake manifold 22 is coupled to a series of combustion chambers 30through a series of intake valves (not shown). The combustion chambersare further coupled to an exhaust manifold 36 via a series of exhaustvalves (not shown). In the depicted embodiment, a single exhaustmanifold 36 is shown. However, in other embodiments, the exhaustmanifold may include a plurality of exhaust manifold sections.Configurations having a plurality of exhaust manifold sections mayenable effluent from different combustion chambers to be directed todifferent locations in the engine system.

In one embodiment, each of the exhaust and intake valves may beelectronically actuated or controlled. In another embodiment, each ofthe exhaust and intake valves may be cam actuated or controlled. Whetherelectronically actuated or cam actuated, the timing of exhaust andintake valve opening and closure may be adjusted for the desiredcombustion and emissions-control performance. For example, the camtiming may be adjusted via a variable cam timing system to move theintake and exhaust cams to a position that provides the optimalvolumetric efficiency for the given operating conditions.

Combustion chambers 30 may be supplied one or more fuels, such asgasoline, alcohol fuel blends, diesel, biodiesel, compressed naturalgas, etc. Fuel may be supplied to the combustion chambers via directinjection, port injection, throttle valve-body injection, or anycombination thereof. In the depicted example, fuel is provided to eachcombustion chamber 30 via direct injection by a fuel injector 66 (whileonly one fuel injector is shown in FIG. 1, each combustion chamberincludes a fuel injector coupled thereto). Fuel may be delivered to fuelinjector 66 by a fuel system (not shown) including a fuel tank, a fuelpump, and a fuel rail. In the combustion chambers, combustion may beinitiated via spark ignition and/or compression ignition.

As shown in FIG. 1, exhaust from exhaust manifold 36 is directed toturbine 116 to drive the turbine. When reduced turbine torque isdesired, a portion of exhaust may be directed instead through awastegate 90, bypassing the turbine. A wastegate actuator 92 (e.g.,wastegate valve) may be actuated open to relieve at least some exhaustpressure from upstream of turbine 116 to a location downstream ofturbine 116 via wastegate 90. By reducing exhaust pressure upstream ofturbine 116, turbine speed may be reduced.

The combined flow from turbine 116 and wastegate 90 flows through anemission control device 170. In general, emission control device 170 mayinclude one or more exhaust after-treatment components configured toreduce an amount of one or more substances in the exhaust flow. Forexample, one exhaust after-treatment component may be configured to trapNO_(x) from the exhaust flow when the exhaust flow is lean and to reducethe trapped NO_(x) when the exhaust flow is rich. In other examples, anexhaust after-treatment component may be configured to disproportionateNO_(x) or to selectively reduce NO_(x) with the aid of a reducing agent.In still other examples, emission control device 170 includes athree-way catalyst configured to oxidize residual hydrocarbons andcarbon monoxide while reducing NO_(x) in the exhaust flow. Differentexhaust after-treatment catalysts having any such functionality may bearranged in wash coats or elsewhere in emission control device 170,either separately or together. In some embodiments, the emission controldevice 170 may further include a regeneratable soot filter configured totrap and oxidize soot particles in the exhaust flow.

All or part of the treated exhaust from emission control device 170 maybe released into the atmosphere via an exhaust conduit 35. Depending onoperating conditions, however, some exhaust may be diverted instead tointake passage 42 via an exhaust gas recirculation (EGR) passage (notshown), including an EGR cooler and an EGR valve. EGR may berecirculated to the inlet of first compressor 110, the inlet of secondcompressor 114, or both.

One or more sensors may be coupled to the inlet of second compressor 114(as shown) and/or first compressor 110 (not shown). For example, atemperature sensor 55 may be coupled to the inlet of second compressor114 for estimating a compressor inlet temperature. As another example, apressure sensor 56 may be coupled to the inlet of second compressor 114for estimating a pressure of air entering the second compressor. Thepressure upstream of second compressor 114 and downstream of firstcompressor 110, as measured by pressure sensor 56, will be hereinreferred to as P₁. Still other sensors may include, for example,air-fuel ratio sensors, humidity sensors, etc. In other examples, one ormore of the second compressor inlet conditions (such as humidity,temperature, etc.) may be inferred based on engine operating conditions.The sensors may estimate a condition of the intake air received at thesecond compressor inlet from the intake passage as well as the airchargerecirculated from upstream of CAC 18. One or more sensors may also becoupled to intake passage 42 upstream of first compressor 110 fordetermining a composition and condition of aircharge entering thecompressor. These sensors may include, for example, a pressure sensor58. The pressure upstream of air box 112 (e.g., barometric pressure), asmeasured by pressure sensor 58, will be herein referred to as P₀. Inaddition, a throttle inlet pressure (TIP) sensor 59 may be coupleddownstream of CAC 18 and upstream of throttle valve 20 for estimating aboost pressure delivered to the engine. The pressure downstream of CAC18 and upstream of throttle valve 20, as measured by TIP sensor 59, willbe herein referred to as P₂. A total pressure ratio across the compoundboosting system is defined as

$\frac{P_{2}}{P_{0}},$a pressure ratio across first compressor 110 is defined as

$\frac{P_{1}}{P_{0}},$and a pressure ratio across second compressor 114 is defined as

$\frac{P_{2}}{P_{1}}.$

During an operator tip-in event, when going from engine operationwithout boost to engine operation with boost responsive to an increasein operator torque demand, turbo lag can occur. This is due to delays inturbine 116 spin-up due to the turbocharger being a slower-actingcompression device, and momentary reduction in flow through secondcompressor 114 when throttle valve 20 opens at the tip-in. The same mayalso occur when the engine is operating boosted and there is a transientincrease in boost demand due to an increase in accelerator pedalapplication by the vehicle operator. To reduce this turbo lag, duringthose selected conditions, both supercharger 13 and turbocharger 15 maybe enabled. In particular, the faster-acting, electrically actuatedcompression device, the electric supercharger, may be used to improvethe transient boost response. Specifically, responsive to the tip-in,waste-gate actuator 92 may be closed (e.g., fully closed) to increaseexhaust flow through turbine 116. While turbine 116 spins-up, boostpressure can be transiently provided by first compressor 110. Enablingsupercharger 13 may include drawing energy from system battery 45 tospin electric motor 108 and thereby accelerate first compressor 110. Inaddition, ESBV 72 may be closed (e.g., fully closed) so as to enable alarger portion of intake air to flow through bypass passage 70 and becompressed by first compressor 110. In addition, CRV 62 may be closed(e.g., fully closed) so as to increase flow through second compressor114. When the turbine has sufficiently spun up and the turbocharger iscapable of providing the requested amount of boost, first compressor 110may be decelerated by disabling electric motor 108 (e.g., bydiscontinuing the supply of power to electric motor 108 from battery45). In addition, ESBV 72 may be opened so as to enable a larger portionof air to bypass first compressor 110. As described further herein,activation (and deactivation) of first compressor 110 may be preciselycontrolled in order to provide the desired boost pressure while reducingovershooting or undershooting of the desired boost pressure, minimizeboost pressure disturbances when first compressor 110 isenabled/disabled, and minimize a duration of operation of firstcompressor 110, thereby minimizing an amount of electrical powerconsumed by supercharger 13. The desired amount of boost may be providedby dynamically coordinating turbocharger 15 and supercharger 13 based onthe boosting capability of turbocharger 15 (e.g., the pressure ratioacross second compressor 114) at a given time and a desired total boostpressure ratio, as described with respect to FIGS. 2-6. Therein, thecontroller may dynamically adjust a pressure ratio allocation to thesupercharger based on a shortfall in airflow incurred at theturbocharger. In addition, the controller may adjust a timing and outputof the motor torque supplied by the electric motor to the superchargerso as to reduce pressure overshoot while maximizing energy recuperation.

During an operator tip-out event, when going from engine operation withboost to engine operation without boost (or reduced boost), compressorsurge may occur. This is due to a decreased flow through the secondcompressor 114 when throttle valve 20 closes at the tip-out. The reducedforward flow through the second compressor can cause surge and degradeturbocharger performance. In addition, surge can lead to noise,vibration, and harshness (NVH) issues such as undesirable noise from theengine intake system. To enable the torque demand to be rapidly reducedresponsive to the tip-out without incurring compressor surge during adefault mode of vehicle operation, at least a portion of the airchargecompressed by second compressor 114 may be recirculated to thecompressor inlet. This allows excess boost pressure to be substantiallyimmediately relieved. In particular, CRV 62 may be opened to recirculate(warm) compressed air from the outlet of second compressor 114, upstreamof CAC 18, to the inlet of second compressor 114. In some embodiments,the compressor recirculation system may additionally or alternativelyinclude a recirculation passage for recirculating cooled compressed airfrom downstream of CAC 18 to the inlet of second compressor 114. Inaddition, wastegate actuator 92 may be moved to a more open (e.g., fullyopen) position so that more of the exhaust flow travels to the tailpipewhile bypassing the turbine, thereby expediting turbine spin-down.

Controller 12 may be included in a control system 14. Controller 12 isshown receiving information from a plurality of sensors 16 (variousexamples of which are described herein) and sending control signals to aplurality of actuators 81 (various examples of which are describedherein). As one example, sensors 16 may include an exhaust gas sensor126 located upstream of turbine 116, MAP sensor 124, an exhausttemperature sensor 128, an exhaust pressure sensor 129, compressor inlettemperature sensor 55, compressor inlet pressure sensor 56 (e.g., formeasuring P₁), a mass air flow (MAF) sensor 57, pressure sensor 58(e.g., for measuring P₀), and TIP sensor 59 (e.g., for measuring P₂).Other sensors, such as additional pressure, temperature, air/fuel ratio,and composition sensors, may be coupled to various locations in enginesystem 100. The actuators 81 may include, for example, throttle valve20, CRV 62, ESBV 72, electric motor 108, wastegate actuator 92, and fuelinjector 66. Controller 12 may receive input data from the varioussensors, process the input data, and employ the various actuators toadjust engine operation based on the received signals and instructionsstored on a memory of the controller. The controller may employ theactuators in response to the processed input data based on instructionor code programmed therein corresponding to one or more routines, suchas example control routines described herein with regard to FIG. 2 (andFIG. 6). As an example, responsive to measured pressures indicating aboost pressure deficiency when operating the turbocharger, thecontroller may actuate the electric motor driving the superchargercompressor and actuate the ESBV closed in order to provide additionalboost via the supercharger compressor.

In this way, the components of FIG. 1 enable a vehicle systemcomprising: an engine having an intake; an accelerator pedal forreceiving an operator torque demand; a compound boost system including afirst (auxiliary) supercharger compressor driven by an electric motorreceiving electrical power from a battery, and a second (primary)turbocharger compressor driven by an exhaust turbine, the secondcompressor positioned downstream of the first compressor in the engineintake; a bypass, including a bypass valve, coupled across the firstcompressor; a waste-gate, including a waste-gate actuator, coupledacross the exhaust turbine; a first pressure sensor coupled to theintake, upstream of the first compressor, to estimate barometricpressure; a second pressure sensor coupled to the intake, downstream ofthe first compressor and upstream of the second compressor, forestimating turbocharger inlet pressure; a third pressure sensor coupledto the intake downstream of the second compressor for estimating athrottle inlet pressure; and a controller with computer readableinstructions stored on non-transitory memory for: responsive to theoperator torque demand, commanding an overall pressure ratio across thecompound boost system via an adjustment to the waste-gate actuator; andvarying the pressure ratio commanded across the first compressor, via anadjustment to an output of the electric motor, based on an airflowshortfall at the second compressor, the airflow shortfall estimatedbased on an actual pressure ratio across the second compressor. In oneexample, commanding the overall pressure ratio may include decreasingthe opening of the waste-gate actuator as the operator torque demandincreases to increase the actual pressure ratio across the secondcompressor, and wherein varying the pressure ratio commanded across thefirst compressor includes operating the electric motor in a motoringmode when the airflow shortfall increases above a threshold, andoperating the electric motor in a generating mode when the airflowshortfall decreases below the threshold. In another example, thecontroller may include further instructions for: closing the ESBV whenthe airflow shortfall increases above a threshold to increase thepressure ratio across the first compressor; and opening the ESBV whenthe airflow shortfall decreases below the threshold to decrease thepressure ratio across the first compressor.

The components of FIG. 1 may further enable the controller to command anoverall pressure ratio for a first compression device of an engineintake based on the operator torque demand; when an actual pressureratio of the second compressor is further from the overall pressureratio, provide positive motor torque to increase the pressure ratio ofthe first compressor; and when the actual pressure ratio of the secondcompressor is closer to the overall pressure ratio, provide negativemotor torque to decrease the pressure ratio of the first compressor. Inthe preceding example, commanding the overall pressure ratio may includedecreasing the opening of the waste-gate actuator as the operator torquedemand increases to increase the actual pressure ratio across the secondcompressor, wherein providing the positive motor torque includesoperating the electric motor in a motoring mode with a motor outputbased on an airflow shortfall, the airflow shortfall estimated based ona difference between the actual pressure ratio of the second compressorand the overall pressure ratio, and wherein providing the negativetorque includes operating the electric motor in a generating mode with agenerator output based on the difference. In a further example, thecontroller may include further instructions for: closing the ESBV whileproviding the positive or negative motor torque. The system may furthercomprise a first pressure sensor coupled to the intake, upstream of thefirst compressor, to estimate barometric pressure; a second pressuresensor coupled to the intake, downstream of the first compressor andupstream of the second compressor, for estimating turbocharger inletpressure; and a third pressure sensor coupled to the intake, downstreamof the second compressor for estimating a throttle inlet pressure;wherein the controller may include further instructions for: estimatingthe overall pressure ratio based on an output of the third pressuresensor relative to the output of the first pressure sensor; estimatingthe actual pressure ratio across the second compressor based on anoutput of the third pressure sensor relative to the output of the secondpressure sensor; and estimating the actual pressure ratio across thefirst compressor based on an output of the second pressure sensorrelative to the output of the first pressure sensor.

Turning now to FIG. 2, an example method 200 for operating a compoundboosted engine system having staged boosting devices is shown. Thecompound boosted engine system may include at least two, seriallyarranged intake compression devices, at least one of which includeselectric assist. One of the at least two compression devices may be aslower acting (lower frequency) compression device, such as aturbocharger configured as the primary boosting device, while anotherother of the two compression devices may be a faster acting (higherfrequency) compression device, such as an electric superchargerconfigured as the auxiliary boosting device. Instructions for carryingout method 200 and the rest of the methods included herein may beexecuted by a controller (e.g., controller 12 of FIG. 1) based oninstructions stored on a memory of the controller and in conjunctionwith signals received from sensors of the engine system, such as thesensors described above with reference to FIG. 1. The controller mayemploy engine actuators of the engine system, such as an electricsupercharger bypass valve (e.g., ESBV 72 of FIG. 1), an electric motor(such as motor 108 of FIG. 1), and a turbocharger wastegate actuator(e.g., wastegate actuator 92 of FIG. 1), to adjust engine operationaccording to the methods described below.

At 202, method 200 includes estimating and/or measuring engine operatingconditions. For example, operating conditions assessed may includeengine speed, pedal position, operator torque demand, manifold absolutepressure, manifold air flow, manifold air temperature, ambientconditions (such as ambient temperature, barometric pressure, andhumidity), engine coolant temperature, etc. For example, barometricpressure may be measured by a pressure sensor, such as pressure sensor58 of FIG. 1.

At 204, method 200 includes determining if boost is requested. In oneexample, boost may be requested at mid-high engine loads. In anotherexample, boost may be requested in response to an operator pedal tip-inor an increase in driver torque demand. If boost is not requested, suchas when the engine load is low or the driver torque demand is low,method 200 proceeds to 206 and includes operating the engine withnatural aspiration (e.g., manifold vacuum). Operating the engine withnatural aspiration may include not activating the staged boostingdevices. For example, an electric motor for driving the electricsupercharger (e.g., electric motor 108) may not be powered, and theturbocharger waste-gate actuator may be commanded fully open in order todirect a portion of exhaust through the waste-gate while bypassing aturbine of the turbocharger (e.g., turbine 116 of FIG. 1). Following206, method 200 ends.

If boost is requested at 204, such as responsive to a tip-in event,method 200 proceeds to 208 and includes generating an overall pressureratio command for the slower, primary compression device based on theoperator torque/boost demand. Herein the overall pressure ratio is asteady-state desired pressure ratio that is commanded to, and achievedby, the primary compression device gradually. The overall pressure ratiocommanded may be defined as

$\frac{P_{2}^{*}}{P_{0}},$where P₂* represents a desired throttle inlet pressure or a desiredpressure at the outlet of the compound boosting system. In one example,this is the pressure at the outlet of the slower-acting primarycompression device, such as the outlet pressure of a turbochargercompressor. P₀ represents an inlet pressure of the compound boostingsystem, or a barometric pressure. In one example, this is the pressureat the inlet of the faster-acting auxiliary compression device, such asthe inlet pressure of an electric supercharger compressor. In aconfiguration where the auxiliary compression device is staged upstreamof the primary compression device, the actual outlet pressure of theprimary compression device, P₂ (e.g., as measured by a TIP sensor), maybe described as:

$\begin{matrix}{P_{2} = {P_{0} \times \frac{P_{1}}{P_{0}} \times \frac{P_{2}}{P_{1}}}} & (1)\end{matrix}$where P₁ is an outlet pressure of the auxiliary compression device,which is also an inlet pressure of the primary compression device. P₂also corresponds to a total boost pressure achieved across the stagedboosting devices. As may be discerned from the above equation,

$\frac{P_{1}}{P_{0}}$is a pressure ratio across the auxiliary compression device and

$\frac{P_{2}}{P_{1}}$is a pressure ratio across the primary compression device. In otherwords, the overall pressure ratio across the system is the product ofthe pressure ratios across each compressor in series. The pressure ratiorepresents the capability of the boosting device (e.g. electricsupercharger, turbocharger or the compound boosting system). However,the throttle inlet pressure cannot separate the boost contribution fromeach device. Thus, by coordinating the pressure ratios commanded to eachboosting device together with a steady-state desired pressure ratioP₂*/P₀, transient boost response can be improved.

In one example, the controller may generate the overall pressure ratiocommand by estimating P₀ based on an output of a barometric pressuresensor. The controller may further estimate P₂* based on an output of anoperator accelerator pedal position sensor. The controller may refer toa look-up table wherein target boost pressure is stored as a function ofpedal position, such as increasing target boost pressure with increaseddepression of the accelerator pedal (increased movement of the pedalposition towards a fully depressed position). Alternatively, thecontroller may use a model or algorithm that uses pedal position as aninput and provides target boost pressure as an output. Then, thepressure ratio command may be determined as P₂*/P₀.

In one example, the turbocharger may be controlled to deliver the entirerequested boost pressure, P₂*. Therefore, the overall pressure ratiocommanded to the turbocharger compressor may be determined as:

$\begin{matrix}{\left. \frac{P_{2}}{P_{1}}\rightarrow\left. {\frac{P_{2}^{*}}{P_{0}}\mspace{14mu}{or}\mspace{14mu} P_{2} \times \frac{P_{0}}{P_{1}}}\rightarrow P_{2}^{*} \right. \right.,{{{when}\mspace{14mu}{\lim\limits_{t\rightarrow\infty}\frac{P_{1}}{P_{0}}}} = 1}} & (2)\end{matrix}$

where t represents time.

At 210, the method includes adjusting a boost pressure actuator of theslower acting primary compression device based on the generated overallpressure ratio command. For example, wherein the primary compressiondevice is a turbocharger, the controller may generate a command for awaste-gate coupled across the exhaust turbine based on the generatedoverall pressure ratio command. The command for the waste-gate may beindicative of a degree of waste-gate valve opening that is sent to awaste-gate actuator. In one example, as the overall pressure ratiocommand increases, the degree of opening of the waste-gate commanded maybe decreased. For example, at higher than threshold pressure ratiocommands, the waste-gate may be fully closed.

In one example, the controller may input the overall pressure ratiocommand and MAF (as determined from an intake MAF sensor) into a look-uptable (or model or algorithm) which outputs a position of theturbocharger waste-gate actuator, the position of the turbochargerwaste-gate actuator corresponding to a turbine speed and a correspondingturbocharger compressor speed. In another example, the controller mayreference a compressor map to determine a desired turbochargercompressor speed for the commanded overall boost pressure ratio and thegiven airflow conditions and may further relate the resultingturbocharger compressor speed to a corresponding position of theturbocharger waste-gate actuator. Further, the actual turbochargerpressure ratio,

$\frac{P_{2}}{P_{1}},$may be used as feed-back for waste-gate control. For example, as theactual turbocharger pressure ratio increases, the turbochargerwaste-gate actuator may be adjusted to a more open position.Additionally or alternatively, if the turbocharger is within a thresholdrange of surge, the openings of one or both of the CRV and thewaste-gate actuator may be increased.

It will be appreciated that in further examples, the commanded overallpressure ratio may be adjusted (e.g., limited) to account for anymechanical constraints of the boosted engine system, such as atemperature, pressure, or speed constraint of the primary compressiondevice, above which (temperature, pressure, or speed) the performance ofthe primary compression device may be adversely affected, such as due tohardware issues. In one example, if the commanded overall pressure ratiobased only on the operator torque demand is predicted to result in acompressor inlet or outlet temperature (of the primary compressiondevice) that is higher than a threshold temperature where the hardwareof the primary compression device is degraded, the controller may reducethe commanded overall pressure ratio with a factor based on thedifference between the predicted temperature and the thresholdtemperature.

Due to the slower response time of the primary compression device,herein the turbocharger, there may be a temporary boost pressuredeficit. For example, the deficit may be due to steady-state boostpressure delivery requiring the turbine to be spun up before it candrive the turbocharger compressor. At 212, the method includesestimating the boost pressure deficit and a corresponding airflowshortfall at the primary compression device. For example, the boostpressure ratio deficit (Π*) of the turbocharger may be defined asfollows:

$\begin{matrix}{\Pi^{*} = \frac{\frac{P_{2}^{*}}{P_{0}}}{\frac{P_{2}}{P_{1}}}} & (3)\end{matrix}$

The controller may calculate the boost pressure deficiency as a function(e.g., ratio or difference) of the actual pressure ratio across theprimary compression device relative to the desired or commanded pressureratio. The actual pressure ratio may be determined as the compressorinlet pressure of the primary compression device relative to the actualthrottle inlet pressure. This boost pressure deficiency reflects theairflow shortfall at the primary compression device and is used toallocate a pressure ratio command to the auxiliary compression device.

For example, where the auxiliary compression device is an electricsupercharger, the pressure ratio commanded to the electric superchargeris dynamically scheduled based on the capability of the turbocharger (asinferred from the actual pressure ratio of the turbocharger, P₂/P₁).This allows the controller to accurately know the exact boost pressuredeficit in real-time, as the turbine is spinning up, and regulate anelectric supercharger speed command (n_eSC) to reduce the deficit. Inaddition, the controller can shape the closed-loop system dynamics byknowing the pressure ratio of the electric supercharger (P₁/P₀), asdescribed herein.

For example, the desired pressure ratio target of the electricsupercharger

$\left( \frac{P_{1}^{*}}{P_{0}} \right)$is defined as Π* with a constraint on the pressure ratio of theturbocharger, as shown as:

$\begin{matrix}{\frac{P_{1}^{*}}{P_{0}} = \frac{\frac{P_{2}^{*}}{P_{0}}}{\max\left\{ {1,\frac{P_{2}}{P_{1}}} \right\}}} & (4)\end{matrix}$

The constraint is included to prevent the desired pressure ratio targetfor the electric supercharger to exceed the total desired systempressure ratio if P₁>P₂, which could happen briefly after an opening ofthe throttle.

At 214, the method includes generating a pressure ratio command for thefaster auxiliary, compression device. In one example, the pressure ratiocommand is generated based on the pressure ratio deficit. In anotherexample, the pressure ratio command is generated based on thecorresponding airflow shortfall. For example, the controller mayestimate an inlet pressure of the electric supercharger (e.g., based ona measured barometric pressure) and use a look-up table, model, oralgorithm to calculate a desired outlet pressure of the electricsupercharger that meets the airflow shortfall. The pressure ratiocommand for the electric supercharger may then be determined as ratio ofthe actual inlet pressure relative to the desired outlet pressure.

At 216, the method includes commanding electric assistance to theauxiliary compression device. In particular, the controller may commandpositive motor torque from the electric motor to auxiliary compressiondevice, such as the electric supercharger, as a function of thedeficit-based pressure ratio command. In one example, commanding thepositive motor torque includes estimating a compressor speed of theelectric compressor that will provide the desired compressor outletpressure at the electric supercharger, such as via a look-up table, map,or algorithm, and then estimating a motor speed of the electric motor(or a degree of electric assistance) that will provide the estimatedcompressor speed. The controller may then adjust a duty cycle commandedto the electric motor to operate the motor at the required motor speed.

Next, at 218, the actual boost pressure may be compared relative to thetarget throttle inlet pressure to determine if the actual boost pressureis within a threshold of the target throttle inlet pressure (TIP). Forexample, it may be determined if the outlet pressure of the turbochargeris within a threshold of the desired TIP, such as when a differencebetween the outlet pressure and the desired TIP is smaller than athreshold. In an alternate example, a ratio of the outlet pressure ofthe turbocharger may be compared to the target throttle inlet pressure.If the difference (or ratio) is not within the threshold, then at 220,the controller continues to dynamically adjust the allocation ofpressure ratios across the primary and auxiliary compression devices. Inparticular, as the turbine spins up and the boosting capability of theturbocharger increases, the pressure ratio across the turbocharger maystart to approach the commanded pressure ratio, the shortfall may startto drop, and accordingly the pressure ratio (and electric assistance)commanded at the electric supercharger may be decreased.

In this way, the controller continually adjusts the auxiliarycompression device in real-time based on the actual capability of theprimary compression device. The controller may use a dynamic allocatedmodule, as further described herein at FIG. 5, to adjust the pressureratios. Consequently, as the slower-responding turbocharger spools up,the desired assist from the faster-responding electric supercharger isgradually phased out. Finally, when the turbocharger is able to sustainthe total desired boost, no assist is required from the electricsupercharger. An example of the dynamic allocation of the pressureratios and the resulting expedited achievement of the target boostpressure with minimal reliance on electric assistance is describedherein with reference to FIG. 3.

Turning briefly to FIG. 3, map 300 depicts pressure ratio across they-axis and time along the x-axis. The overall commanded pressure ratiowhich is based on the torque demand, represented by P*₂/P₀, is depictedby dashed line 302. As such, this is the pressure ratio commanded to theprimary compression device. The actual pressure ratio of the primarycompression device, represented by P₂/P₁, is depicted by dashed line304, and is indicative of the primary compression device's boostingcapability. This changes over time and builds to the steady-state valuethat was commanded gradually due to the primary compression device'sslower response time. An interim pressure ratio deficit, represented byπ*(unclipped), is depicted by dashed line 306. The clipped version ofthis pressure ratio deficit is used to schedule the pressure ratiocommanded to the auxiliary compression device, which has the fasterresponse time. The pressure ratio commanded to the auxiliary compressiondevice, represented by P*₁/P₀, is depicted by solid line 308.

Responsive to the torque demand, an overall pressure ratio command 302is determined and commanded to the primary compression device. However,due to the slow response time of the primary compression device (e.g.,turbo lag), the actual pressure ratio 304 achieved at the primarycompression device is lower, and initially the pressure ratio deficit306 may be significant. If this pressure ratio deficit is not addressed,the transient boost response is adversely affected. The pressure ratiodeficit is met by commanding a pressure ratio 308 to the auxiliarycompression device. In particular, during the initial part of the boostresponse, a larger portion of the overall pressure ratio is dynamicallyallocated to the auxiliary compression device due to the larger pressureratio deficit incurred at the primary compression device. Then, as theprimary compression device spins up, a larger portion of the overallpressure ratio is delivered by the primary compression device, and thecontribution of auxiliary compression device is dynamically reduced byphasing out the pressure ratio commanded to the auxiliary compressiondevice. As a result, the overall reliance on electric assistance isminimized while improving the transient boost response.

Returning to FIG. 2, at 218, if the boost pressure is within thethreshold of the target TIP, but still below the target TIP, then at222, the method includes providing negative motor torque from theelectric motor to the auxiliary compression device. This allows theboost pressure to coast to the target TIP, reducing the likelihood ofpressure overshoot. In addition, electric assistance from the motor isreduced earlier, improving fuel economy. Furthermore, by operating themotor as a generator in a region where pressure overshoot could occur,energy recuperation via the motor is enabled, further improving fueleconomy while also improving the boost response. The controller may usea lead compensator module, as further described herein at FIG. 5, todetermine the timing (e.g., in relation to turbine speed or boostpressure) at which electric assistance from the motor is discontinuedand when the motor is transitioned to being operated as a generator. Inone example, the motor may be spun as a generator at a speed that isbased on the predicted overshoot. The routine then ends.

As mentioned earlier, the compound boosting system can be described as:

$\begin{matrix}{P_{2} = {P_{0}*\frac{P_{1}}{P_{0}}*\frac{P_{2}}{P_{1}}}} & (5)\end{matrix}$where P₀ is the inlet pressure to the first boosting device and P₁, P₂are the outlet pressure from the first and second boosting device (TIP).P₁*, P₂* denote the desired pressure target for the first and secondboosting device. In the configuration described above, the firstboosting device is a transient (auxiliary) device, such as the electricsupercharger, and the second boosting device is the main device, such asthe turbocharger. The control reference of the first boosting device isdetermined as:

$\begin{matrix}{\frac{P_{1}^{*}}{P_{0}} = {{\frac{P_{2}^{*}}{P_{0}}*\min\left\{ {1,\frac{P_{1}}{P_{2}}} \right\}\mspace{14mu}{or}\mspace{14mu} P_{1}^{*}} = {P_{2}^{*}*\min\left\{ {1,\frac{P_{1}}{P_{2}}} \right\}}}} & (6)\end{matrix}$

A clip is included to prevent the desired pressure target for the firstboosting device to exceed that of the second boosting device if P₁>P₂,which could happen briefly after an opening of the throttle. The mainboosting device is required to deliver the entire desired boostpressure. Therefore, the target for the second device P₂* is always toprovide the full pressure ratio (from ambient) regardless of the stateof the auxiliary device. In this case:

$\begin{matrix}{\left. \frac{P_{2}}{P_{1}}\rightarrow\left. {\frac{P_{2}^{*}}{P_{0}}\mspace{14mu}{or}\mspace{14mu} P_{2}*\frac{P_{0}}{P_{1}}}\rightarrow P_{2}^{*} \right. \right.,{{{when}\mspace{14mu}{\lim\limits_{t\rightarrow\infty}\frac{P_{1}}{P_{0}}}} = 1}} & (7)\end{matrix}$

As such, a base controller can be overwritten to not operate theauxiliary boosting device or operate the auxiliary boosting device in acontinuous fashion, and vice versa for the main boosting device.

If the controller is calibrated conservatively to minimize P₂ overshoot,boost pressure response may become slower than the maximum systemcapability. Therefore, by using a lead compensator together withaggressive calibration of the controller, the transient response of theboosting system is improved. In the meantime, the lead compensator willrequest a speed reduction before P₂ approaches P₂*. The command enablesthe energy recuperation mode of the electric motor, maximizing thewindow for energy recuperation.

The lead compensator in Laplace domain can be expressed as:

$\frac{Y(S)}{U(S)} = \frac{{\alpha\; s} + 1}{{\tau\; s} + 1}$

Input U is the pressure ratio error of the electric supercharger:

$U = {\frac{P_{1}^{*}}{P_{0}} - \frac{P_{1}}{P_{0}}}$

To implement in the discrete system, the following conversion isderived:

$x_{k} = {{{\left( {1 - f} \right)x_{k - 1}} + {{fu}_{k,}f}} = \frac{T_{s}}{\tau + T_{S}}}$${y_{k} = {{\left( {1 - r} \right)x_{k}} + {ru}_{k}}},{r = {\frac{\alpha}{\tau} \geq 1}}$where f is the time constant in discrete domain, r is the lead ratio,and T_(s) is the execution rate.

The output of the lead compensator is clipped for allowing specificationof the range of lead actions on U in increasing or decreasingdirections.

=clip(u _(k)−Δ₁ ,y _(k) ,u _(k)+Δ₂)

An example of the lead compensation of the pressure ratio at theelectric supercharger and the resulting reduction in pressure overshootand expedited enablement of energy recuperation at the electric motor isdescribed herein with reference to FIG. 4.

Turning briefly to FIG. 4, map 400 depicts how lead compensation is usedalong with dynamic pressure ratio allocation to improve transient boostresponse while maximizing energy recuperation opportunities. Map 400includes maps 402 and 404. Map 404 depicts changes in an electric assistcommanded to an electric supercharger (across the y-axis) over time(along the x-axis) in relation to the allocation of a pressure ratio(across the y-axis) over the same time frame (along the x-axis) betweena turbocharger and an electric supercharger, represented at map 402. Theoverall commanded pressure ratio which is based on the torque demand,represented by P₂*/P₀, is depicted by solid line 408. As such, this isthe pressure ratio commanded to the primary compression device, herein aturbocharger. The actual pressure ratio achieved via the compound boostsystem, represented by P₂/P₀, without lead compensation (w/o LC) isdepicted by plot 410, and is to be compared to P₂/P₀ achieved with leadcompensation (with LC), depicted by plot 412. The motor speed commandedto the electric supercharger without lead compensation (w/o LC) is shownat plot 430 and is to be compared to motor speed command with leadcompensation (with LC), depicted by plot 434. The portion of the motorspeed command received via the lead compensator module of the controlleris shown at plot 432.

Prior to t1, the engine is operating without boost and therefore thecommanded pressure ratio is low. At t1, responsive to an increase inoperator torque demand, the boost pressure requirement increases. As aresult, the overall pressure ratio command (408) that is generated basedon the torque demand increases. This is the signal that is commanded tothe turbocharger for steady-state achievement of a target TIP. However,due to the slow response time of the turbocharger, there is a temporarypressure ratio deficit that is met by actuating the electricsupercharger and dynamically allocating a larger portion of the overallcommanded pressure ratio the electric supercharger. In particular, att1, a pressure ratio command is delivered to the electric superchargeras a function of the boost pressure (for example, based on thecorresponding airflow deficit) that results from the slow response ofthe turbocharger. In accordance, the motor speed of the electricsupercharger is increased (430, 434) which results in an increase in thepressure ratio across the supercharger. At this time, the electric motoris operating in a motor mode to provide energy to the supercharger.

As the turbine spins up, it is able to account for a larger portion ofthe overall pressure ratio command. After t2, when the pressure ratio atthe turbocharger is within a threshold of the overall pressure ratio,but still below the overall pressure ratio, the lead compensator modulesends a signal (432) to the electric motor to decrease the motor speedand provide negative motor torque. At this time, the electric motor isoperating in a generating mode to recuperate energy from thesupercharger. As a result of the timing of the lead compensation beforethe target overall pressure ratio is attained, the pressure ratio at theturbocharger (412) coasts to the target pressure ratio. If the leadcompensation were not provided, the pressure ratio at the turbocharger(410) would overshoot the overall pressure ratio (that is, P₂/P₀ wouldexceed P₂*/P₀), resulting in a torque error. This may affectdrivability. Also, as a result of the timing of the lead compensationbefore the target overall pressure ratio is attained, the pressure ratioat the supercharger is decreased in a timely manner. If the leadcompensation were not provided, the pressure ratio at the supercharger(420) would also overshoot the commanded pressure ratio (that is, P₁/P₀would exceed P₁*/P₀). Not only would this result in a drop in fueleconomy due to the electric supercharger being operated for longer thanrequired, but an additional drop in fuel economy would occur due to themissed energy recuperation opportunity. Instead, by providing the leadcompensation earlier, the pressure overshoot is addressed by absorbingtorque at the motor. As a result, the overall transient response of theboosted engine is improved while also extending the window of energyrecuperation for the electric motor.

It will be appreciated that the electric supercharger may be thetransient device that is not controlled continuously. A supervisorycontroller may coordinate operation of the electric supercharger and theelectric supercharger bypass valve. The main objective of thesupervisory controller may be to determine when to activate anddeactivate the electric supercharger and electric supercharger bypassvalve to meet control requirements, subject to system constraints andhardware protection. At a high level, the electric supercharger isactivated and the bypass valve closed when the activation criteria ismet and no system faults are observed. Once the deactivation criteriaare met or system faults are observed, the electric supercharger isdeactivated and the bypass valve is opened.

There may be several considerations in the design of the activationstrategy. First, the controller may activate the electric superchargeronly when necessary, such as when the vehicle drivability isunacceptable because of the slow response of the turbocharger. Second,proactive action may be desired if the strategy does not have to waituntil unacceptable drivability is observed. Lastly, the controller aimsto reduce unwanted activation for driver change-of-mind events.

Since the boost pressure ratio deficit (Π*) can be used as an index todetermine the driver demand deficit (that represents the drivability),the proactive action can be achieved by looking at the rate of change ofΠ*, and the threshold (f₂) for activation is determined as a function ofΠ* as follows:

$\frac{d\left( \Pi^{*} \right)}{dt} > {f_{2}\left( \Pi^{*} \right)}$

Two first order low pass filters (H_(lp)) on both the Π* and

$\frac{d\left( \Pi^{*} \right)}{dt}$are added to mitigate “false positive” activation during the driverchange-of-mind events, such as when the driver aggressively presses theacceleration pedal but rapidly removes the command, as follows:

$H_{{{lp}\_ k}_{1,2}} = {{{\left( {1 - h_{1,2}} \right)H_{{{lp}\_ k}_{1,2} - 1}} + {h_{1,2}\Pi_{k}^{*}\mspace{14mu} h_{1,2}}} = \frac{T_{s}}{\tau_{1,2} + T_{S}}}$where h_(1,2) are the two time constants in the discrete domain.

The activation strategy is illustrated via a sample accelerationtrajectory at FIG. 7. The trajectories shown at map 700 are constructedwith X-axis depicting the filtered boost pressure deficit and the Y-axisdepicting the filtered rate of change of the boost pressure deficit. Theactivation threshold depicted by solid line 702, is determined as afunction of the filtered Π*. The acceleration trajectory when electricassist from the electric motor is not required is shown by clear circles706. The acceleration trajectory when electric assist from the electricmotor is required is shown by filled circles 704. The calibration showsthat the electric supercharger will be activated when the rate of changeof the Π* is high, even when the absolute Π* is low. On the other hand,if Π* is gradually developed to reach an unacceptable level, thestrategy will activate the electric supercharger. The main criteria todeactivate the electric supercharger is when the turbocharger is able tosustain the desired boost, or the boost pressure deficit is reduced andbelow a threshold, such as when:Π*≤αwhere α is a calibratable constant.

It will be appreciated that while the examples discussed above pertainto a configuration including a turbocharger coupled to an electricsupercharger, this is not meant to be limiting. In other examples, theturbocharger may be configured with electric assistance (e.g., as ane-turbo having an electric motor coupled to the compressor, the turbine,or the turbocharger shaft). Further examples may pertain to boostedengines have staged superchargers or stages turbochargers, at least oneof which has electric assistance.

Turning now to FIG. 5, a block diagram of an example controlarchitecture for a compound boosting system having a higher frequencycompression device with electric assistance and a lower frequencycompression device is shown. For example, the control architecture maybe applied to an engine system having an electric superchargercompressor (e.g., first compressor 110 of FIG. 1) coupled to an engineintake passage upstream of a turbocharger compressor (e.g., secondcompressor 114 of FIG. 1). The control architecture may be utilized by acontroller (e.g., controller 12 of FIG. 1) while performing a controlmethod, such as method 200 of FIG. 2, in order to regulate boostpressure delivery.

The electric supercharger controller (C₁) includes a dynamic allocator(D₁) that apportions the desired boost pressure control reference; astate machine (A₁) that manages the operation of electric superchargersystem; a closed-loop controller (I₁) that consists of a model basedfeed forward function (F₁), and a feedback controller (H₁) forcalculating the desired electric supercharger speed command.

The feed forward control action (n_(eSC_ff)) of the electricsupercharger is based on the steady state compressor map provided by thesupplier. The compressor map is converted to look up desired compressorspeed based on the inputs of corrected mass flow ({dot over (m)}_(corr))and desired pressure ratio

$\left( \frac{P_{1}^{*}}{P_{0}} \right).$

$\begin{matrix}{n_{e{SC}\_{ff}} = {f_{1}\left( {\frac{P_{1}^{*}}{P_{0}},{\overset{.}{m}}_{corr}} \right)}} & (8)\end{matrix}$

Mass flow ({dot over (m)}) is estimated as the desired cylinder airflow, then corrected to the reference pressure (P_(ref)) and temperature(T_(ref)).

$\begin{matrix}{{\overset{.}{m}}_{corr} = \frac{\overset{.}{m}\sqrt{\frac{T_{0}}{T_{ref}}}P_{0}}{P_{ref}}} & (9)\end{matrix}$

The desired boost pressure reference of the electric supercharger isobtained from the desired throttle inlet pressure (P₂*) that isprocessed by a high pass filter (H₁). The frequencies that pass throughthe high pass filter are the frequencies that the turbocharger is notable to respond to, in other words, the deficit of the turbochargercapability. A closed-loop control C₁ determines the desired speedcommand (n_(eSC)) of the electric supercharger. C₂ is the controller forturbocharger that determines the wastegate position (θ_(wg)). Because ofthe dynamics between waste-gate and the turbocharger speed, there isgenerally not a need to add a low pass filter to P₂* for turbochargercontrol, but one can be added as necessary. Also, C₂ is designed suchthat the waste-gate is saturated during large transients and only tunesthe response when throttle inlet pressure is approaching to the desiredtarget. At that time, control actions from C₁ are greatly reducedbecause of the high pass filter that ensures minimum interaction betweenthe two actuators.

A proportional feedback controller (H₁) is implemented to account forplant model (the electric supercharger compressor map) mismatch.Steady-state boost tracking is designed to be delivered by the mainturbocharger. Therefore, there is no integral action in the feedbackcontroller. A lead compensator is added to shape the closed-loop controlresponse since the inner loop electric supercharger speed controller mayhave a different bandwidth for controlling the speed in increasing ordecreasing directions.

Supervisory controller (A₁) is developed to coordinate the electricsupercharger and electric supercharger bypass valve. The main objectiveof the supervisory controller is to determine when to activate anddeactivate the electric supercharger and electric supercharger bypassvalve to meet control requirements, subject to system constraints andhardware protection. At a high level, the electric supercharger will beactivated and the bypass valve closed when the activation criteria ismet and no system faults are observed. Once the deactivation criteria ismet or system faults are observed, the electric supercharger will bedeactivated and the bypass valve opens.

A desired boost pressure ratio across both compressors

$\left( \frac{P_{2}^{*}}{P_{0}} \right)$along with a measured (e.g., achieved) pressure ratio across theturbocharger compressor

$\left( \frac{P_{2}}{P_{1}} \right)$are input into the dynamic allocator D₁. The pressure ratio across theturbocharger compressor may be controlled by turbocharger controller C₂which receives the desired boost pressure ratio across both compressorsas well as the measured pressure ratio across the turbochargercompressor as feedback. Controller C₂ then produces a signal foradjusting a degree of opening of a turbocharger waste-gate actuator(θ_(wg)), which is then sent to the turbocharger G₂, resulting in thepressure ratio across the turbocharger compressor

$\frac{P_{2}}{P_{1}}.$Thus, the opening of the turbocharger waste-gate actuator may becontrolled based on the desired boost pressure ratio and the achievedpressure ratio across the turbocharger compressor. For example, as thedesired boost pressure ratio increases, the degree of opening of thewaste-gate actuator may be decreased in order to flow a greater portionof exhaust gas through a turbine of the turbocharger and not through theturbocharger waste-gate actuator, thereby increasing a speed of theturbine and, as a result, the pressure ratio across the turbochargercompressor.

Dynamic allocator D₁ uses the pressure ratio across the turbochargercompressor and the overall desired boost pressure ratio to calculate adesired pressure ratio

$\left( \frac{P_{1}^{*}}{P_{0}} \right)$for the supercharger compressor, for example, using the functionsdescribed above. The desired pressure ratio for the supercharger as wellas measured pressures P₀ and P₂ and desired boost pressure P₂* are inputinto a state machine A₁, which is a supervisory controller for adiscrete event system. State machine A₁ determines whether P₂ isdeficient enough (e.g., greater than a threshold deficiency) to triggeractivation of the electric supercharger. Additionally, there are othercriteria that ensure that electric supercharger operation would notviolate other engine system constraints, for example, due to faults,temperature, electric power availability, etc. Hysteresis is also addedto the activation criteria as:

${\frac{P_{2}^{*}}{P_{0}} - \frac{P_{2}}{P_{1}}} \geq {hysteresis}$to avoid on/off cycling of the system.

Once electric supercharger activation is triggered, the desiredsupercharger compressor pressure ratio together with a desired mass flow({dot over (m)}) are input into a model-based feedforward controller F₁.For example, model-based feed-forward controller F₁ may look up acorresponding supercharger compressor speed from a compressor map. Thecorresponding supercharger compressor speed, n_(eSC_ff), is then outputto an adder element 518.

The desired supercharger compressor pressure ratio is also input into anadder element 520 along with a feedback signal concerning the actualsupercharger compressor pressure ratio

$\left( \frac{P_{1}}{P_{0}} \right),$which is subtracted from the desired supercharger compressor pressureratio as part of an outer loop control C₁. The result is input into anerror feedback controller to fine-tune the supercharger compressor speedas well as regulate any inaccuracies of the compressor map. A feedbackresponse concerning the supercharger compressor speed, n_(eSC_fb),generated by the error feedback controller is then input to the adderelement 518, which outputs the electric supercharger compressor speedn_(eSC) for the given operating conditions. The electric superchargercompressor speed may be transformed into a corresponding electric signal(e.g., duty cycle) that is applied to an electric motor of electricsupercharger G₁ to produce the pressure ratio across the superchargercompressor

$\left( \frac{P_{1}}{P_{0}} \right).$Thus, the supercharger compressor speed may be continuously updatedbased on

$\frac{P_{2}^{*}}{P_{0}}\mspace{14mu}{and}\mspace{14mu}\frac{P_{2}}{P_{1}}$and, more specifically, a deficit between

$\frac{P_{2}}{P_{1}}\mspace{14mu}{and}\mspace{14mu}{\frac{P_{2}^{*}}{P_{0}}.}$

Turning now to FIG. 6, an example method 600 for operating a boostedengine system having an electric supercharger (e.g., supercharger 13 ofFIG. 1) staged upstream of a turbocharger (e.g., turbocharger 15 of FIG.1), is shown. Herein, the turbocharger is configured as a main boostingdevice, and the supercharger is configured as an auxiliary boostingdevice.

At 602, method 200 includes estimating and/or measuring engine operatingconditions. For example, operating conditions assessed may includeengine speed, pedal position, operator torque demand, manifold absolutepressure, manifold air flow, manifold air temperature, ambientconditions (such as ambient temperature, barometric pressure, andhumidity), engine coolant temperature, etc. For example, barometricpressure may be measured by a pressure sensor, such as pressure sensor58 of FIG. 1.

At 604, method 600 includes determining if boost is requested. In oneexample, boost may be requested at mid-high engine loads. In anotherexample, boost may be requested in response to an operator pedal tip-inor an increase in driver torque demand. If boost is not requested, suchas when the engine load is low or the driver torque demand is low,method 600 proceeds to 606 and includes operating the engine withnatural aspiration (e.g., manifold vacuum). Operating the engine withnatural aspiration may include not activating the staged boostingdevices. For example, an electric motor for driving the electricsupercharger (e.g., electric motor 108) may not be powered, and theturbocharger wastegate actuator may be commanded fully open in order todirect a portion of exhaust through the wastegate while bypassing aturbine of the turbocharger (e.g., turbine 116 of FIG. 1). Following606, method 600 ends.

If boost is requested at 604, such as responsive to a tip-in event,method 600 proceeds to 608 and includes generating a desired pressureratio (e.g., a target pressure ratio) command for the turbocharger basedon the boost demand. The desired pressure ratio, defined as

$\frac{P_{2}^{*}}{P_{0}},$is a ratio of a desired outlet pressure of a compressor of theturbocharger (e.g., second compressor 114 of FIG. 1), which is alsoequal to the desired boost pressure (or desired TIP), relative to P₀which represents an inlet pressure of a compressor of the electricsupercharger (e.g., first compressor 110 of FIG. 1). For example, P₀ maybe equal to barometric pressure (e.g., as measured by pressure sensor 58of FIG. 1).

At 610, the method includes decreasing an opening of the turbochargerwaste-gate based on the overall pressure ratio command. For example, asthe pressure ratio command increases, the waste-gate opening may bedecreased. In one example, the waste-gate is fully closed. By closingthe turbocharger waste-gate, all of the exhaust flow may be directedthrough the turbocharger turbine, expediting spin-up of the turbine.Optionally, a compressor recirculation valve (such as CRV 62 of FIG. 1)may also be closed so that pressure loss across the turbochargercompressor is reduced. Thereafter compressed air is flowed to the enginevia the turbocharger compressor. At this time, the electric superchargerbypass valve is open, causing the air to flow to the turbochargercompressor while bypassing the supercharger.

At 612, the method includes calculating a boost pressure deficiency atthe turbocharger. The boost pressure deficiency may be determined by aboost pressure shortfall (P₂*−P₂), which is a difference between thedesired boost pressure and the measured throttle inlet pressure, as wellas a rate of change of the boost pressure shortfall

$\left( \frac{d\left( {P_{2}^{*} - P_{2}} \right)}{dt} \right).$For example, the turbocharger may be unable to achieve the desired boostpressure due to turbo lag, as described with respect to FIG. 2. Thecontroller may also determine an air flow shortfall at the turbocharger(inlet) corresponding to the boost pressure deficiency or use pressureratios rather than delta pressures. In alternate examples, the boostpressure deficiency is based on a ratio of the desired boost pressureand the measured throttle inlet pressure instead of the difference. Inother words, the boost pressure deficiency is based on the desired boostpressure relative to the measured throttle inlet pressure.

At 614, responsive to the indication of a boost pressure deficit beingpresent, the method includes closing the ESBV. By (fully) closing theESBV, the electric supercharger compressor may be included in the intakeflow path and intake air is flowed to the turbocharger compressor viathe electric supercharger. That is, airflow through the superchargercompressor is increased. In other examples, the ESBV may be closedresponsive to the amount of the boost pressure deficiency, such asresponsive to the amount being greater than a threshold, such as athreshold above which transient boost response is adversely affected.For example, it may be determined if an absolute amount of the boostpressure deficiency is greater than the threshold, or if a rate ofchange of the boost pressure shortfall,

$\frac{d\left( {P_{2}^{*} - P_{2}} \right)}{dt},$is greater than the threshold, with the threshold calibrated as afunction of the boost pressure shortfall:

$\frac{d\left( {P_{2}^{*} - P_{2}} \right)}{dt} > {f_{2}\left( {P_{2}^{*} - P_{2}} \right)}$with ƒ₂ representing a function. For example, the threshold may decreaseas the boost pressure shortfall increases. The threshold may define anallowable amount of boost pressure deficiency above which engine peakpower and torque performance may be degraded. Further, the threshold maybe set such that, above the threshold, an amount of additional power andtorque provided by operating the electric supercharger outweighs anamount of electricity consumed by the electric supercharger.Additionally, both the boost pressure shortfall and the rate of changeof the boost pressure shortfall may be run through a first order lowpass filter. By filtering the boost pressure shortfall and/or the rateof change of the boost pressure shortfall, unnecessary activation of thesupercharger compressor may be reduced, such as due to driver change ofmind (e.g., applying an accelerator pedal for less than a thresholdduration). If the boost pressure deficiency is not greater than thethreshold, the ESBV may be maintained open, the electric superchargermay remain deactivated, and compressed air may flow to the engine viaonly the turbocharger compressor while bypassing the superchargercompressor.

At 616, responsive to the boost pressure deficiency, the method includesoperating the electric supercharger compressor using electric assist toimprove transient boost response. Actuating the electric motor coupledto the supercharger compressor serves to accelerate the superchargercompressor, thereby increasing the boost pressure provided to theengine. For example, accelerating the supercharger compressor mayinclude spinning the supercharger compressor via the electric motorusing power drawn from a battery (e.g., system battery 45 of FIG. 1).Therefore, the supercharger may be able to provide boost for a limitedduration, the duration limited by the state of charge of the systembattery powering the electric motor. An amount of power (or duty cycleof power) commanded to the electric motor may be based on a pressureratio allocated to the supercharger as a function of the deficit. Forexample, the controller may determine a desired supercharger pressureratio based on the airflow shortfall. The controller may further inputthe computed supercharger pressure ratio and MAF into a look-up table todetermine the desired supercharger compressor speed. The controller maythen input the supercharger compressor speed into an additional look-uptable or function to output the motor speed, and a corresponding amountof power (or duty cycle of power) to provide to the electric motor, toproduce the target pressure ratio across the supercharger.

The desired supercharger pressure ratio,

$\frac{P_{1}^{*}}{P_{0}},$may be clipped to prevent the desired pressure target of thesupercharger (P₁*) from exceeding that desired of the turbocharger if P₁is greater than P₂, which may occur briefly after an opening of thethrottle. Thus, a control reference for the supercharger compressor maybe described as:

$\frac{P_{1}^{*}}{P_{0}} = {{\frac{P_{2}^{*}}{P_{0}} \times \min\left\{ {1,\frac{P_{1}}{P_{2}}} \right\}\mspace{14mu}{or}\mspace{14mu} P_{1}^{*}} = {P_{2}^{*} \times \min\mspace{14mu}\left\{ {1,\frac{P_{1}}{P_{2}}} \right\}}}$which is also equal to the pressure ratio deficit (or pressure deficit,if P₁* is determined instead of

$\left. \frac{P_{1}^{*}}{P_{0}} \right)$of the turbocharger compressor. That is, the supercharger compressor maybe controlled based on the turbocharger boost pressure ratio deficit (orboost pressure deficit) in order to provide the desired boost pressureratio

$\frac{P_{2}^{*}}{P_{0}}$(or boost pressure P₂*). Thereafter compressed air flows to the enginevia the turbocharger compressor and the supercharger compressor. Assuch, the outlet pressure of the turbocharger compressor, P₂, containspressure generated by both the supercharger compressor and theturbocharger compressor.

At 618, the method includes determining if the actual boost pressureachieved at the outlet of the turbocharger is within a threshold of thetarget boost pressure or TIP. The threshold may be determined as afunction of the target TIP or the overall commanded pressure ratio andmay be adjusted to reduce the possibility of pressure overshoot. Forexample, at higher pressure ratios, the threshold may be larger.

If the actual boost pressure is lower than the desired TIP by more thanthe threshold amount, then at 622, the method includes continuing toprovide electric assistance via the supercharger while providing thesteady-state boost pressure via the turbocharger. For example, thecontroller may maintain or further decrease (if possible) the opening ofthe waste-gate. In addition, the controller may maintain or furtherincrease (if possible) the motor speed of the electric motor.

When the actual boost pressure is lower than the desired TIP by only thethreshold amount, the controller may apply the lead compensation anddiscontinue electric assistance. In particular, the motor speed of theelectric motor may be decreased so as to coast the boost pressure to thetarget TIP with reduced overshoot. In addition, the controller maytransition the motor to a generator mode and operate the generator toapply a negative torque on the supercharger compressor, therebydecelerating the supercharger compressor and recuperating the energywhich would have otherwise caused the boost pressure overshoot.

At 624, it may be confirmed that the target boost pressure has beenreached. If the target boost pressure is not reached, at 626, the methodincludes further adjusting the waste-gate opening and/or the generatorspeed. For example, the actuators may be adjusted to provide a targetspeed profile or trajectory to the target boost pressure. Else, if thetarget boost pressure has been reached, at 628, the method includesdisabling the motor/generator. Therein, the electric motor coupled tothe supercharger compressor may be disabled through a signal sent fromthe controller to an electromechanical actuator of the motor thatreduces motor rotation speed. Additionally, the ESBV may be actuatedopen (e.g., fully open) to allow intake air to flow to engine, via theturbocharger compressor while bypassing the supercharger compressor.Thereafter, compressed air may be supplied to the engine by theturbocharger compressor only and not via the supercharger compressor.

In this way, by transiently and dynamically operating the superchargercompressor based on the turbocharger compressor pressure ratio, boostpressure deficiencies (e.g., due to delays in spinning up theturbocharger turbine) are reduced. Further, an amount of time thesupercharger is activated and drawing power is minimized, reducingelectric power consumption and increasing fuel economy. Following 628,the method ends.

FIG. 8 depicts a prophetic example graph 800 of dynamic allocation ofpressure ratios to provide coordinated turbocharger and electricsupercharger control during vehicle operation, such as according to themethod of FIG. 2 (and FIG. 6) and using the control architecture of FIG.5. Accelerator pedal position is shown in plot 802, actual throttleinlet pressure (TIP) is shown at solid line plot 806 relative to thedesired TIP at dashed line plot 805, an achieved pressure ratio across aturbocharger compressor

$\left( \frac{P_{2}}{P_{1}} \right)$is shown in plot 808 relative to a desired overall boost pressure ratio

$\left( \frac{P*_{2}}{P_{0}} \right)$shown in plot 804, a turbine speed of the turbocharger is shown in plot810, an achieved pressure ratio across the electric superchargercompressor

$\left( \frac{P_{1}}{P_{0}} \right)$is shown in plot 812, a commanded electric supercharger motor speed isshown in plot 816 while plot 817 shows generator activation, a degree ofopening of an electric supercharger bypass valve (ESBV) is shown in plot818, and a degree of opening of a turbocharger waste-gate is shown inplot 820. For all of the above, the X-axis represents time, with timeincreasing along the X-axis from left to right. The Y-axis representsthe labeled parameter, with values increasing from bottom to top. In thepresent example, the electric supercharger compressor is locatedupstream of the turbocharger compressor, such as in the engine system ofFIG. 1.

Prior to time t1, the engine is operated without boost (plot 806) due toa lower driver demand (plot 802) requiring a lower TIP (plot 805). Thus,the actual turbocharger compressor (TC) pressure ratio (plot 808) andthe electric supercharger compressor ratio (plot 812) are at a baselineamount (e.g., approximately 1), indicating that the pressure upstream ofeach compressor is equal to the pressure downstream of each compressordue to air not being compressed by either compressor. Because theelectric supercharger (ES) is not activated, the commanded speed of theelectric supercharger compressor remains at zero (plot 816) and the ESBVis fully open (plot 818). Thereby, intake air bypasses the electricsupercharger compressor instead of being directed to the electricsupercharger compressor, as described further with respect to FIG. 1.Further, the turbocharger waste-gate is fully open (plot 820), keepingthe turbocharger turbine speed low (plot 810) due to exhaust bypassingthe turbine through the open waste-gate.

At time t1, the operator tips in, as shown by the increase inaccelerator pedal position (plot 802), moving the engine from operationwith natural aspiration to operation with boost. A desired amount ofboost pressure, as reflected by a rise in desired TIP (plot 805) isdetermined based on the amount of driver-demanded torque, and theoverall pressure ratio desired across the boosted engine system (plot804) increases accordingly. The turbocharger is controlled via a commandbased on the overall desired boost pressure ratio. To provide thedesired overall boost pressure ratio in steady-state, the turbochargerwaste-gate is fully closed (plot 820), thereby directing all of theexhaust through the turbocharger turbine (and not through theturbocharger waste-gate) in order to spin up the turbine. As a result,the turbine speed (plot 810) begins to increase. However, due to theslow response time of the turbine speed, the turbocharger is unable toachieve the desired overall pressure ratio (see difference between plots804 and 808) and the desired TIP. The actual turbocharger compressorpressure ratio (plot 808) is below the desired overall boost pressureratio (plot 804) between time t1 and time t2.

A pressure ratio deficiency and a corresponding air flow deficiency atthe turbocharger is determined based on desired overall pressure ratio(804) relative the actual boost pressure ratio at the turbocharger (808)(e.g., based on the difference as in this example or based on a ratio).A pressure ratio corresponding to the air flow deficiency is thencommanded to the supercharger compressor (plot 812) so that thecombination of the pressure ratio across the supercharger compressor(plot 812) and the pressure ratio across the turbocharger compressor(plot 808), together, can meet the overall desired boost pressure ratio(plot 804). Thus, between t1 and t2, when the turbine speed is lower, alarger portion of the overall boost pressure ratio is allocated to thesupercharger since a smaller portion is delivered by the turbocharger.

Responsive to the boost pressure deficiency being greater than thethreshold, the electric supercharger is activated shortly after time t1to fill the deficiency while the turbine spins up. Activating theelectric supercharger includes closing the ESBV (plot 818) to directintake air to the electric supercharger compressor and supplying powerto an electric motor driving the compressor at a duty cycle thatoperates the electric motor at a speed (plot 816) that is based on theboost pressure deficit of the turbocharger compressor. In particular,the commanded speed of the electric motor coupled to the superchargercompressor is selected so that the desired pressure ratio across thesupercharger compressor can be provided. The desired electricsupercharger compressor pressure ratio increases as the boost pressuredeficit at the turbocharger compressor increases. Between time t1 andtime t2, a larger portion of the total boost pressure ratio (plot 806)is provided by the boost pressure generated by the electricsupercharger, with the electric supercharger pressure ratio rapidlyincreasing (plot 812) as the electric motor is activated. A smallerportion of the total boost pressure ratio is provided by theturbocharger pressure ratio (plot 808) due to the lower turbochargerturbine speed (plot 810).

Between time t1 and time t2, the turbine spins up slowly (plot 810).However, the pressure ratio across the turbocharger compressor (plot808) continues to lag behind the total achieved boost pressure ratio(plot 806). Between time t2 and time t3, the turbine speed (plot 810)increases faster, with a corresponding increase in the pressure ratioacross the turbocharger compressor (plot 808) and a correspondingdecrease in the boost pressure deficiency. As the pressure ratio acrossthe turbocharger compressor (plot 808) increases, the pressure ratioacross the supercharger compressor decreases so that the achieved totalboost pressure ratio (plot 806) equals the desired boost pressure ratio.Then, once the achieved total boost pressure ratio (plot 806) is closeto the desired boost pressure ratio (804), the pressure ratio across thesupercharger compressor is gradually decreased (via adjustments to aduty cycle of the electric motor) as the pressure ratio across theturbocharger compressor increases. Between t2 and t3, an increasingportion of the total boost pressure ratio (plot 806) is provided by theboost pressure generated by turbocharger and a remaining portion isprovided by the boost pressure generated by the electric supercharger.

At time t3, actual TIP (plot 806) is within a threshold of the desiredTIP (plot 805) due to the boost pressure generated by both theturbocharger compressor and the electric supercharger compressor. Toreduce a boost pressure overshoot, between t3 and t4, the controllerapplies lead compensation to reduce the electric motor speed before P₂approaches P₂*. In particular, before actual TIP reaches the target TIP,the electric motor brakes the compressor so as to reduce thesupercharger compressor speed and ES pressure ratio. The generatorcommand (plot 817) implies that the motor is operated in a generatormode, which enables energy recuperation at the electric motor/generatorcoupled to the supercharger compressor. The turbocharger waste-gate maystart to open between time t3 and time t4 (plot 820). If this leadcompensation were not provided, TIP would have overshot the desiredvalue, causing torque errors, and an energy recuperation opportunitywould have been lost.

At time t4, the turbocharger compressor pressure ratio (plot 808)reaches the desired total pressure ratio (plot 804). Therefore, thedesired pressure ratio across the supercharger compressor (plot 812) isreduced to a baseline amount (e.g., approximately 1) and the electricsupercharger is deactivated (e.g., no power is supplied to the electricmotor driving the supercharger compressor). The ESBV is opened (plot818) to direct intake air directly to the turbocharger compressor andnot to the supercharger compressor, and the commanded electricsupercharger speed (plot 816) is reduced to zero. As the superchargercompressor spins down, the pressure ratio across the superchargercompressor (plot 812) returns to baseline. Further, the degree ofopening of the turbocharger wastegate actuator is increased (plot 820)in response to the turbocharger compressor boost pressure ratio (plot808) reaching the desired boost pressure ratio (plot 804). Thus, theturbine speed (plot 810) is maintained to provide the desired boostpressure target with feedback concerning the achieved turbochargercompressor boost pressure ratio (plot 808).

At time t5, the accelerator pedal position decreases (plot 802). As aresult, the desired total boost pressure ratio decreases accordingly(plot 804). To reduce boost pressure, the turbocharger wastegateactuator (plot 820) is further opened to decelerate the turbochargerturbine (plot 810) and thereby the turbocharger compressor. As a result,the achieved pressure ratio across the turbocharger compressor (plot808) decreases. Further, because the electric supercharger is disabled,the turbocharger compressor is supplying all of the boost pressure.

At time t6, the accelerator pedal position further decreases (plot 802),for example, due to a tip-out event. The desired total boost pressureratio (plot 804) decreases down to baseline, as boost is no longerrequested based on the driver demand. The turbocharger waste-gate isfully opened (plot 820) to reduce the boost pressure, thereby furtherdecelerating the turbocharger turbine (plot 810) down to a baselinespeed. The speed of the turbocharger compressor decreases accordingly,decreasing the amount of boost pressure produced by the turbochargercompressor. As a result, the pressure ratio across the turbochargercompressor (plot 808) decreases to the baseline (e.g., approximately 1).As described above, because the turbocharger compressor is supplying allof the boost pressure, the total boost pressure ratio (plot 806) alsodecreases to the baseline.

In this way, a turbocharger compressor, coupled downstream of asupercharger compressor, may be operated via a waste-gate adjustment toprovide an overall pressure ratio between an inlet of the superchargercompressor and an outlet of the turbocharger compressor based onoperator torque demand while operation of the supercharger compressor isdynamically adjusted, via adjustment of an electric motor, based on areal-time pressure ratio (or airflow) shortfall at the turbochargercompressor. Herein, operating the turbocharger compressor via thewaste-gate adjustment may include, as the operator boost demandincreases, decreasing an opening of the waste-gate to spin up an exhaustturbine of the turbocharger and increase the overall pressure ratio. Ina further example, the real-time pressure (or airflow) shortfall at theturbocharger compressor may be estimated based on an actual pressureratio across the turbocharger compressor relative to the desired overallpressure ratio, the actual pressure ratio across the turbochargercompressor changing as the exhaust turbine spins up. An enginecontroller may adjust operation of the supercharger compressor byincreasing a positive motor torque provided from the electric motor tothe supercharger compressor to increase a supercharger compressor speedas the airflow shortfall increases, while maintaining an actual pressureratio across the supercharger compressor below a threshold pressureratio based on the desired overall pressure ratio, and further based onthe actual pressure ratio across the turbocharger compressor. Further,responsive to a difference (or ratio) between actual throttle inletpressure and a target throttle inlet pressure based on the operatorboost demand being higher than a threshold, the controller may increasea negative motor torque provided from the electric motor to thesupercharger compressor to decrease the supercharger compressor speed.In another example, responsive to a boost pressure overshoot, the speedof the supercharger compressor may be reduced by providing negativemotor torque from the electric motor while maintaining the decreasedopening of the waste-gate. In comparison, responsive to a boost pressureundershoot, the speed of the supercharger compressor may be increased byproviding additional positive motor torque from the electric motor whilefurther decreasing the opening of the waste-gate. Adjusting operation ofthe supercharger compressor based on the airflow shortfall may include,as an example, adjusting an output of the supercharger compressorindependent of a position of the waste-gate and independent of a turbinespeed of the turbocharger.

In this way, while providing boost with a turbocharger of a compoundboosting system, an electric supercharger may be activated in responseto a boost pressure deficiency in order to achieve a desired boostpressure, with both the turbocharger and the electric superchargercontrolled based on pressure ratio measurements. The technical effect ofdynamically adjusting the pressure ratio allocation to the electricsupercharger based on the boosting capability of the turbocharger, inreal-time, is that transient boost response can be improved. Inparticular, the electric supercharger may be activated only as long asrequired to support the turbocharger, minimizing electric assistancedrawn from the supercharger. By conserving electric power usage, fueleconomy is improved. By calibrating the pressure ratio commanded to theelectric supercharger and the turbocharger more aggressively, boostdemand can be met more expediently. By providing a positive motor torqueto the electric supercharger when the boosting capability of theturbocharger is the actual boost pressure is lower, turbo lag can beaddressed. The technical effect of transitioning to providing a negativemotor torque when the boost pressure is within a threshold distance ofthe target pressure, is that the boost pressure may be coasted to thetarget pressure without incurring any pressure overshoot. In addition,the energy recuperation ability of the electric motor is improved.Overall, boost pressure can be provided rapidly and more efficiently.

An example method comprises: commanding an overall pressure ratio for afirst compression device of an engine intake based on operator torquedemand; and adjusting a timing of electric engagement provided to asecond compression device of the engine intake based on an airflowshortfall at the first compression device. In the preceding example,additionally or optionally, the method further comprises adjusting anamount of the electric engagement provided to the second compressiondevice of the engine intake based on the airflow shortfall at the firstcompression device. In any or all of the preceding examples,additionally or optionally, the timing and amount of the electricengagement is adjusted to dynamically vary a pressure ratio across thesecond compression device. In any or all of the preceding examples,additionally or optionally, the adjusting includes, operating theelectric motor in a motor mode to provide positive motor torque to thesecond compression device while the airflow shortfall at the firstcompression device is higher than a threshold, and operating theelectric motor in a generator mode to provide negative motor torque tothe second compression device while the airflow shortfall at the firstcompression device is smaller than the threshold. In any or all of thepreceding examples, additionally or optionally, providing positive motortorque to the second compression device includes accelerating the secondcompression device and increasing the pressure ratio across the secondcompression device, and wherein providing negative motor torque to thesecond compression device includes decelerating the second compressiondevice and decreasing the pressure ratio across the second compressiondevice. In any or all of the preceding examples, additionally oroptionally, the threshold is based on the overall pressure ratiocommanded to the first compression device, and wherein during theelectric engagement, a throttle inlet pressure is below a target boostpressure based on the operator torque demand. In any or all of thepreceding examples, additionally or optionally, the adjusting furtherincludes, responsive to the throttle inlet pressure being at the targetboost pressure, disabling the electric engagement. In any or all of thepreceding examples, additionally or optionally, the first compressiondevice is a turbocharger, the second compression device is an electricsupercharger, and wherein the first compression device is stageddownstream of the second compression device in the engine intake. In anyor all of the preceding examples, additionally or optionally, commandingan overall pressure ratio for the first compression device includesadjusting an opening of an exhaust waste-gate valve coupled across anexhaust turbine of the turbocharger. In any or all of the precedingexamples, additionally or optionally, the airflow shortfall is estimatedin real-time based on an actual pressure ratio across the firstcompression device relative to the commanded overall pressure ratio, theactual pressure ratio across the turbocharger compressor changing as theexhaust turbine spins up.

Another example method comprises: adjusting operation of a first intakecompression device based on a target boost pressure; commanding positivetorque from an electric motor to a second intake compression devicewhile a difference between an outlet pressure of the first compressiondevice and the target boost pressure is higher than a threshold; andcommanding negative torque from the electric motor to the second intakecompression device while the difference is smaller than the threshold.In the preceding example, additionally or optionally, the first intakecompression device is a turbocharger having a slower response time thanthe second intake compressor device, and wherein the adjusting includescommanding an overall pressure ratio for the first intake compressiondevice based on the target boost pressure, and adjusting an opening of awaste-gate valve coupled across an exhaust turbine of the turbochargerbased on the commanded overall pressure ratio. In any or all of thepreceding examples, additionally or optionally, while commanding boththe positive torque and the negative torque, the outlet pressure of thefirst compression device is below the target boost pressure. In any orall of the preceding examples, additionally or optionally, the methodfurther comprises, in response to the outlet pressure of the firstcompression device being at the target boost pressure, disabling theelectric motor. In any or all of the preceding examples, additionally oroptionally, the second compression device is an electric superchargerand wherein the commanding includes dynamically varying a pressure ratioacross the second compression device via the negative torque or thepositive torque while maintaining the pressure ratio across the secondcompression device less than a desired pressure ratio across the firstcompression device. In any or all of the preceding examples,additionally or optionally, commanding the positive torque includesestimating an airflow shortfall at the first compression device, inreal-time, based on the difference between the outlet pressure of thefirst compression device and the target boost pressure; and increasing acompressor speed of the second compression device via the positivetorque as the estimated airflow shortfall increases.

Another example vehicle system comprises: an engine having an intake; anaccelerator pedal for receiving an operator torque demand; a compoundboost system including a first supercharger compressor driven by anelectric motor receiving electrical power from a battery, and a secondturbocharger compressor driven by an exhaust turbine, the secondcompressor positioned downstream of the first compressor in the engineintake; a bypass, including a bypass valve, coupled across the firstcompressor; a waste-gate, including a waste-gate actuator, coupledacross the exhaust turbine; and a controller with computer readableinstructions stored on non-transitory memory for: commanding an overallpressure ratio for the second compressor based on the operator torquedemand; when an actual pressure ratio of the second compressor isfurther from the overall pressure ratio, providing positive motor torqueto increase a pressure ratio of the first compressor; and when theactual pressure ratio of the second compressor is closer to the overallpressure ratio, providing negative motor torque to decrease the pressureratio of the first compressor. In the preceding example, additionally oroptionally, commanding the overall pressure ratio includes decreasingthe opening of the waste-gate actuator as the operator torque demandincreases to increase the actual pressure ratio across the secondcompressor, wherein providing the positive motor torque includesoperating the electric motor in a motoring mode with a motor outputbased on an airflow shortfall, the airflow shortfall estimated based ona difference between the actual pressure ratio of the second compressorand the overall pressure ratio, and wherein providing the negativetorque includes operating the electric motor in a generating mode with agenerator output based on the difference. In any or all of the precedingexamples, additionally or optionally, the controller includes furtherinstructions for: closing the ESBV while providing the positive and thenegative motor torque. In any or all of the preceding examples,additionally or optionally, the system further comprises a firstpressure sensor coupled to the intake, upstream of the first compressor,to estimate barometric pressure; a second pressure sensor coupled to theintake, downstream of the first compressor and upstream of the secondcompressor, for estimating turbocharger inlet pressure; a third pressuresensor coupled to the intake, downstream of the second compressor forestimating a throttle inlet pressure; and wherein the controllerincludes further instructions for: estimating the overall pressure ratiobased on an output of the third pressure sensor relative to the outputof the first pressure sensor; estimating the actual pressure ratioacross the second compressor based on an output of the third pressuresensor relative to the output of the second pressure sensor; andestimating the actual pressure ratio across the first compressor basedon an output of the second pressure sensor relative to the output of thefirst pressure sensor.

In a further representation, the controller may include furtherinstructions for estimating the actual pressure ratio across the firstcompressor based on an output of the second pressure sensor relative tothe output of the first pressure sensor; estimating the actual pressureratio across the second compressor based on the output of the thirdpressure sensor relative to the output of the second pressure sensor;and estimating the overall pressure ratio of the engine intake based onthe output of the third pressure sensor relative to the output of thefirst pressure sensor.

In another further representation, a method for a boosted engine systemincludes directing an overall pressure ratio command to a turbocharger;and dynamically adjusting allocation of a portion of the overallpressure ratio command to the supercharger based on an airflow shortfallat the turbocharger compressor, the airflow shortfall based on turbinespeed. In the preceding example, additionally or optionally, thedirecting an overall pressure ratio command to the turbocharger includesa waste-gate adjustment. In any or all of the preceding examples,additionally or optionally, the airflow shortfall is estimated based onan actual pressure ratio at the turbocharger relative to the overallpressure ratio command, the actual pressure ratio inferred from theturbine speed.

Note that the example control and estimation routines included hereincan be used with various engine and/or vehicle system configurations.The control methods and routines disclosed herein may be stored asexecutable instructions in non-transitory memory and may be carried outby the control system including the controller in combination with thevarious sensors, actuators, and other engine hardware. The specificroutines described herein may represent one or more of any number ofprocessing strategies such as event-driven, interrupt-driven,multi-tasking, multi-threading, and the like. As such, various actions,operations, and/or functions illustrated may be performed in thesequence illustrated, in parallel, or in some cases omitted. Likewise,the order of processing is not necessarily required to achieve thefeatures and advantages of the example embodiments described herein, butis provided for ease of illustration and description. One or more of theillustrated actions, operations and/or functions may be repeatedlyperformed depending on the particular strategy being used. Further, thedescribed actions, operations and/or functions may graphically representcode to be programmed into non-transitory memory of the computerreadable storage medium in the engine control system, where thedescribed actions are carried out by executing the instructions in asystem including the various engine hardware components in combinationwith the electronic controller.

It will be appreciated that the configurations and routines disclosedherein are exemplary in nature, and that these specific embodiments arenot to be considered in a limiting sense, because numerous variationsare possible. For example, the above technology can be applied to V-6,I-4, I-6, V-12, opposed 4, and other engine types. The subject matter ofthe present disclosure includes all novel and non-obvious combinationsand sub-combinations of the various systems and configurations, andother features, functions, and/or properties disclosed herein.

The following claims particularly point out certain combinations andsub-combinations regarded as novel and non-obvious. These claims mayrefer to “an” element or “a first” element or the equivalent thereof.Such claims should be understood to include incorporation of one or moresuch elements, neither requiring nor excluding two or more suchelements. Other combinations and sub-combinations of the disclosedfeatures, functions, elements, and/or properties may be claimed throughamendment of the present claims or through presentation of new claims inthis or a related application. Such claims, whether broader, narrower,equal, or different in scope to the original claims, also are regardedas included within the subject matter of the present disclosure.

The invention claimed is:
 1. A method, comprising: operating a firstcompression device of an engine intake based on operator torque demand;and while operating the first compression device: operating an electricmotor in a motor mode to provide positive motor torque to a secondcompression device of the engine intake while an airflow shortfall atthe first compression device is higher than a threshold; operating theelectric motor in a generator mode to provide negative motor torque tothe second compression device while the airflow shortfall at the firstcompression device is smaller than the threshold; and disconnecting thesecond compression device, bypassing the second compression device byopening a bypass valve of the second compression device, and providingcompressed air via only the first compression device when there issubstantially no airflow shortfall at the first compression device. 2.The method of claim 1, wherein providing positive motor torque to thesecond compression device includes accelerating the second compressiondevice and increasing a pressure ratio across the second compressiondevice, and wherein providing negative motor torque to the secondcompression device includes decelerating the second compression deviceand decreasing the pressure ratio across the second compression device.3. The method of claim 1, wherein the threshold is based on an overallpressure ratio commanded to the first compression device, and whereinthe airflow shortfall occurs when a throttle inlet pressure is less thana target boost pressure, where the target boost pressure is determinedbased on the operator torque demand.
 4. The method of claim 3, whereinthe first compression device is a turbocharger, the second compressiondevice is an electric supercharger, and wherein the first compressiondevice is staged downstream of the second compression device in theengine intake.
 5. The method of claim 4, wherein commanding the overallpressure ratio for the first compression device includes adjusting anopening of an exhaust waste-gate valve coupled across an exhaust turbineof the turbocharger.
 6. The method of claim 5, wherein the airflowshortfall is estimated in real-time based on an actual pressure ratioacross the first compression device relative to the commanded overallpressure ratio, the actual pressure ratio across the turbochargerchanging as the exhaust turbine spins up.
 7. A method, comprising:adjusting operation of a first intake compression device based on atarget boost pressure; and while adjusting operation of the first intakecompression device: commanding positive torque from an electric motor toa second intake compression device while a difference between an outletpressure of the first intake compression device and the target boostpressure is higher than a threshold; commanding negative torque from theelectric motor to the second intake compression device while thedifference is smaller than the threshold; and disabling the electricmotor and bypassing the second intake compression device when the outletpressure of the first intake compression device reaches the target boostpressure.
 8. The method of claim 7, wherein the first intake compressiondevice is a turbocharger having a slower response time than the secondintake compression device, and wherein the adjusting operation of thefirst intake compression device includes: commanding an overall pressureratio for the first intake compression device based on the target boostpressure, and adjusting an opening of a waste-gate valve coupled acrossan exhaust turbine of the turbocharger based on the commanded overallpressure ratio.
 9. The method of claim 8, wherein while commanding boththe positive torque and the negative torque, the outlet pressure of thefirst intake compression device is below the target boost pressure. 10.The method of claim 8, wherein the second intake compression device isan electric supercharger and wherein the commanding positive torque andthe commanding negative torque include dynamically varying a pressureratio across the second intake compression device while maintaining thepressure ratio across the second intake compression device less than adesired pressure ratio across the first intake compression device. 11.The method of claim 8, wherein commanding the positive torque includes:estimating an airflow shortfall at the first intake compression device,in real-time, based on the difference between the outlet pressure of thefirst intake compression device and the target boost pressure; andincreasing a compressor speed of the second intake compression devicevia the positive torque as the estimated airflow shortfall increases.12. A vehicle system, comprising: an engine having an intake; anaccelerator pedal for receiving an operator torque demand; a compoundboost system including a first turbocharger compressor driven by anexhaust turbine, the first turbocharger compressor positioned downstreamof a second supercharger compressor in the engine intake, the secondsupercharger compressor driven by an electric motor receiving electricalpower from a battery; a bypass, including a bypass valve, coupled acrossthe second supercharger compressor; a waste-gate, including a waste-gateactuator, coupled across the exhaust turbine; and a controller withcomputer readable instructions stored on non-transitory memory for:commanding an overall pressure ratio for the first turbochargercompressor based on the operator torque demand; adjusting a timing of anelectric engagement provided to the second supercharger compressor, theadjusting the timing including when an actual pressure ratio of thefirst turbocharger compressor is further from the overall pressureratio, providing positive motor torque to increase a pressure ratio ofthe second supercharger compressor; and when the actual pressure ratioof the first turbocharger compressor is closer to, but not yet at, theoverall pressure ratio, providing negative motor torque to decrease thepressure ratio of the second supercharger compressor; and when theactual pressure ratio of the first turbocharger compressor reaches theoverall pressure ratio, disabling the second supercharger compressor andopening the bypass valve to bypass the second supercharger compressorwhile still providing compressed air via the first turbochargercompressor based on operator torque demand.
 13. The system of claim 12,wherein commanding the overall pressure ratio includes decreasing anopening of the waste-gate actuator as the operator torque demandincreases to increase the actual pressure ratio across the firstturbocharger compressor, wherein providing the positive motor torqueincludes operating the electric motor in a motoring mode with a motoroutput based on an airflow shortfall, the airflow shortfall estimatedbased on a difference between the actual pressure ratio of the firstturbocharger compressor and the overall pressure ratio, and whereinproviding the negative torque includes operating the electric motor in agenerating mode with a generator output based on the difference.
 14. Thesystem of claim 13, wherein the controller includes further instructionsfor: closing the bypass valve while providing the positive and thenegative motor torque.
 15. The system of claim 13, further comprising: afirst pressure sensor coupled to the intake, upstream of the secondsupercharger compressor, to estimate barometric pressure; a secondpressure sensor coupled to the intake, upstream of the firstturbocharger compressor and downstream of the second superchargercompressor, for estimating turbocharger inlet pressure; a third pressuresensor coupled to the intake, downstream of the first turbochargercompressor for estimating a throttle inlet pressure; and wherein thecontroller includes further instructions for: estimating the overallpressure ratio based on an output of the third pressure sensor relativeto an output of the first pressure sensor; estimating the actualpressure ratio across the first turbocharger compressor based on theoutput of the third pressure sensor relative to an output of the secondpressure sensor; and estimating the actual pressure ratio across thesecond supercharger compressor based on the output of the secondpressure sensor relative to the output of the first pressure sensor.